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Pricing Products and Services Appendix A PowerPoint Authors: Susan Coomer Galbreath, Ph.D., CPA Charles W. Caldwell, D.B.A., CMA Jon A. Booker, Ph.D., CPA, CIA Cynthia J. Rooney, Ph.D., CPA Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. Appendix A-2 The Economists’ Approach to Pricing Elasticity of Demand The price elasticity of demand measures the degree to which the unit sales of a product or service are affected by a change in unit price. Change Change in versus in Unit Price Sales Appendix A-3 Price Elasticity of Demand Demand for a product is inelastic if a change in price has little effect on the number of units sold. Example The demand for designer perfumes sold at cosmetic counters in department stores is relatively inelastic. Appendix A-4 Price Elasticity of Demand Demand for a product is elastic if a change in price has a substantial effect on the number of units sold. Example The demand for gasoline is relatively elastic because if a gas station raises its price, unit sales will drop as customers seek lower prices elsewhere. Appendix A-5 Price Elasticity of Demand As a manager, you should set higher (lower) markups over cost when demand is inelastic (elastic) Appendix A-6 Price Elasticity of Demand ln(1 + % change in quantity sold) Єd = ln(1 + % change in price) Price elasticity of demand Natural log function I can estimate the price elasticity of demand for a product or service using the above formula. Appendix A-7 Price Elasticity of Demand Suppose the managers of Nature’s Garden believe that every 10 percent increase in the selling price of its apple-almond shampoo will result in a 15 percent decrease in the number of bottles of shampoo sold. Let’s calculate the price elasticity of demand. Apple Almond For its strawberry glycerin soap, managers of Nature’s Garden believe that the company will experience a 20 percent decrease in unit sales if its price is increased by 10 percent. Appendix A-8 Price Elasticity of Demand For Nature’s Garden apple-almond shampoo. ln(1 + % change in quantity sold) Єd = ln(1 + % change in price) Єd = ln(1 + (-0.15)) ln(1 + (0.10)) Apple Almond Єd = ln(0.85) = -1.71 ln(1.10) Appendix A-9 Price Elasticity of Demand For Nature’s Garden strawberry glycerin soap. ln(1 + % change in quantity sold) Єd = ln(1 + % change in price) Єd = ln(1 + (-0.20)) ln(1 + (0.10)) Єd = ln(0.80) = -2.34 ln(1.10) Appendix A-10 Price Elasticity of Demand The price elasticity of demand for the strawberry glycerin soap is larger, in absolute value, than the apple-almond shampoo. This indicates that the demand for strawberry glycerin soap is more elastic than the demand for apple-almond shampoo. Apple Almond Appendix A-11 The Profit-Maximizing Price Under certain conditions, the profit-maximizing price can be determined using the following formula: Profit-maximizing markup on = variable cost -1 1 + Єd Using the above markup, the selling price would be set using the formula: Variable -1 Profit-maximizing ) × cost per = (1 + price 1 + Єd unit Appendix A-12 The Profit-Maximizing Price Let’s determine the profit-maximizing price for the apple-almond shampoo sold by Nature’s Garden. The shampoo has a variable cost per unit of $2.00. Price elasticity of demand = -1.71 Apple Almond Profit-maximizing markup = on variable cost -1.00 = 1.41 or 141% 1 + (-1.71) Variable cost per unit x Markup (1 + 1.41) Profit-maximizing price $ 2.00 2.41 $4.82 Appendix A-13 The Profit-Maximizing Price Now let’s turn to the profit-maximizing price for the strawberry glycerin soap sold by Nature’s Garden. The soap has a variable cost per unit of $0.40. Price elasticity of demand = -2.34 Profit-maximizing markup = on variable cost -1.00 = 0.75 or 75% 1 + (-2.34) Variable cost per unit x Markup (1 + .75) Profit-maximizing price $ $ 0.40 1.75 0.70 Appendix A-14 The Profit-Maximizing Price Apple Almond The 75 percent markup for the strawberry glycerin soap is lower than the 141 percent markup for the apple-almond shampoo. This is because the demand for strawberry glycerin soap is more elastic than the demand for apple-almond shampoo. Appendix A-15 The Profit-Maximizing Price Nature’s Garden is currently selling 200,000 bars of strawberry glycerin soap per year at the price of $0.60 a bar. If the change in price has no effect on the company’s fixed costs or on other products, let’s determine the effect on contribution margin of increasing the price by 10 percent. Appendix A-16 The Profit-Maximizing Price Contribution margin will increase by $1,600. Sales price Units sales Sales Variable cost Contribution margin Present Price $ 0.60 200,000 Higher Price $ 0.66 160,000 $ $ $ 120,000 80,000 40,000 † $0.60 + (0.10 × $0.60) = $0.66 ‡ 200,000 - (0.20 × 200,000) = 160,000 $ 105,600 64,000 41,600 † ‡ Appendix A-17 The Cost Base Under the absorption approach to cost-plus pricing, the cost base is the absorption costing unit product cost rather than the variable cost. The cost base includes direct materials, direct labor, and variable and fixed manufacturing overhead. Appendix A-18 Setting a Target Selling Price Here is information provided by the management of Ritter Company. Direct materials Direct labor Variable manufacturing overhead Fixed manufacturing overhead Variable S & A expenses Fixed S & A expenses Per Unit $ 6 4 3 Total $ 70,000 2 60,000 Assuming Ritter will produce and sell 10,000 units of the new product, and that Ritter typically uses a 50% markup percentage, let’s determine the unit product cost. Appendix A-19 Setting a Target Selling Price The first step in the absorption costing approach to cost-plus pricing is to compute the unit product cost. Direct materials Direct labor Variable manufacturing overhead Fixed manufacturing overhead Unit product cost Per Unit $ 6 4 3 7 $ 20 ($70,000 ÷ 10,000 units = $7 per unit) Ritter has a policy of marking up unit product costs by 50%. Let’s calculate the target selling price. Appendix A-20 Setting a Target Selling Price The second step is to calculate the target selling price ($30) by assigning the appropriate markup ($10) to the unit product cost ($20). Direct materials Direct labor Variable manufacturing overhead Fixed manufacturing overhead Unit product cost 50% markup Target selling price Per Unit $ 6 4 3 7 $ 20 10 $ 30 Appendix A-21 Determining the Markup Percentage A markup percentage can be based on an industry “rule of thumb,” company tradition, or it can be explicitly calculated. The equation for calculating the markup percentage on absorption cost is shown below. Markup % on absorption cost = (Required ROI × Investment) + S & A expenses Unit sales × Unit product cost The markup must be high enough to cover S & A expenses and to provide an adequate return on investment. Appendix A-22 Determining the Markup Percentage Let’s assume that Ritter must invest $100,000 in the product and market 10,000 units of product each year. The company requires a 20% ROI on all investments. Let’s determine Ritter’s markup percentage on absorption cost. Appendix A-23 Determining the Markup Percentage Markup % (20% × $100,000) + ($2 × 10,000 + $60,000) on absorption = 10,000 × $20 cost Variable S & A per unit Total fixed S & A Markup % on absorption cost = ($20,000 + $80,000) $200,000 = 50% Appendix A-24 Setting a Target Selling Price Now assign the calculated markup ($10) to the unit product cost ($20) to arrive at Price. Direct materials Direct labor Variable manufacturing overhead Fixed manufacturing overhead Unit product cost 50% markup Target selling price Per Unit $ 6 4 3 7 $ 20 10 $ 30